## Kurtosis

The degree of peakedness of a distribution, also called the Excess or Excess Coefficient. Kurtosis is denoted (or ) or and computed by taking the fourth Moment of a distribution. A distribution with a high peak is called Leptokurtic, a flat-topped curve is called Platykurtic, and the normal distribution is called Mesokurtic. Let denote the th Moment . The Fisher Kurtosis is defined by

 (1)

and the Pearson Kurtosis is defined by
 (2)

An Estimator for the Fisher Kurtosis is given by
 (3)

where the s are k-Statistic. The Standard Deviation of the estimator is
 (4)

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Moments of a Distribution: Mean, Variance, Skewness, and So Forth.'' §14.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 604-609, 1992.